Database Reference
In-Depth Information
A
confidence interval
is an interval estimate of a population parameter or
characteristic based on sample data. A confidence interval is used to indicate the
uncertainty of a point estimate. If is the estimate of some unknown population
mean , the confidence interval provides an idea of how close is to the unknown
. For example, a 95% confidence interval for a population mean straddles the
TRUE
, but unknown mean 95% of the time. Consider
Figure 3.25
as an example.
Assume the confidence level is 95%. If the task is to estimate the mean of an
unknown value
in a normal distribution with known standard deviation
and
the estimate based on observations is , then the interval
straddles the
unknown
Figure 3.25
A 95% confidence interval straddling the unknown population mean
μ
value of with about a 95% chance. If one takes 100 different samples and
computes the 95% confidence interval for the mean, 95 of the 100 confidence
intervals will be expected to straddle the population mean
.
Confidence intervals appear again in Section 3.3.6 on ANOVA. Returning to the
discussion of hypothesis testing, a key assumption in both the Student's and
Welch's
t
-test is that the relevant population attribute is normally distributed. For
non-normally distributed data, it is sometimes possible to transform the collected
data to approximate a normal distribution. For example, taking the logarithm of
a dataset can often transform skewed data to a dataset that is at least symmetric
around its mean. However, if such transformations are ineffective, there are tests
like the Wilcoxon rank-sum test that can be applied to see if two population
distributions are different.
